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Abstract

Tracking trajectories of objects is conventionally achieved by direct beam probing or by sequential imaging of the target during its evolution. However, these strategies fail quickly when the direct line of sight is inhibited. Here, we propose and experimentally demonstrate real-time tracking of objects, which are completely surrounded by scattering media that practically conceal the objects. We show that full 3D motion can be effectively encoded in the statistical properties of spatially diffused but temporally coherent radiation. The method relies on measurements of integrated scattered intensity performed anywhere outside the disturbance region, which renders flexibility for different sensing scenarios as well as low-light capabilities.

Figures (8)

Tracking a hidden target enclosed in a “scattering box” that impedes direct imaging. A coherent source of radiation generates a spatially and temporally varying field that illuminates the target. Fluctuations of the integrated intensity are detected outside the enclosure and are used to track the target position.

Schematic illustration of using (a) the memory effect associated with the light propagating through the scattering wall and (b) the increase of the illumination speckle size used to encode the transversal and axial motions of the target, respectively.

(a) Image of a laser beam with beam waist of d≈520μm scattered at the front and back walls of the box. The scale bar is 2.5 cm. (b) Amplitude of the autocorrelation function |Ci(τ)| of the recorded intensity corresponding to different target transversal displacements Δx. The decorrelation time (black band) depends linearly on the target transversal motion, as expected from Eq. (5). The lower left inset illustrates the linear relation between the decorrelation time and the target transversal motion. The upper right inset shows the approximately 5mm×5mm size object under uniform illumination.

(a) Integrated intensity variance spectrum for varying secondary source size d. The dotted red curve indicates the shift in the variance spectrum as a function of the axial motion of a target for ±2mm. The green dot shows the optimum secondary source size d0≈520μm. (b) Linear dependency of the integrated intensity variance as a function of the target axial displacement for d=d0. For clarity, all measured variances are normalized by the value of the maximum variance.

(a) Experimental demonstration of 3D tracking: the blue line represents the imposed target displacement, while the red dashed line indicates the reconstructed trajectory. (b) One-dimensional representations of the imposed and recovered trajectories shown in (a), where tm denotes one measurement duration. The solid blue line denotes the exact trajectory, while the dashed red line indicates the reconstructed trajectory. Also, see Visualization 1.

Experimental demonstration of 3D tracking using a priori calibrations to extract the constants in Eq. (7). The blue line represents the imposed target displacement, while the red dashed line indicates the reconstructed trajectory.

Evolution of the relative error ε/⟨Δr⟩ during the tracking procedure. The error in reconstructing the target location is evaluated as ε2(t)=εx2(t)+εy2(t)+εz2(t), and ⟨Δr⟩ denotes the average step size in moving the target. The solid line and the shaded area indicate the average and the standard deviation of the error over one hundred trajectories.

Error evolution in recovering an absolute trajectory. The time variable is normalized by the measurement time tm. The error in reconstructing the target location is evaluated as ε2(t)=εx2(t)+εy2(t)+εz2(t). The solid line and the shaded area show the average and the standard deviation of errors over one hundred trajectories, respectively.